Math Problem Statement
Forty families were surveyed and asked to record the number of hours per week their television was in use. The results are shown in this frequency table. Number of Hours Frequency 0-9 1 10-19 6 20-29 15 30-39 12 40-49 2 50-59 4
Which histogram is an accurate representation of the data? a. A histogram has frequency on the x-axis, and number of hours on the y-axis. 0 to 9 is 8, 10 to 19 is 2, 20 to 29 is 10, 30 to 39 is 12, 40 to 49 is 4, 50 to 59 is 2. b. A histogram has number of hours on the x-axis, and frequency on the y-axis. 0 to 9 is 1, 10 to 19 is 6, 20 to 29 is 15, 30 to 39 is 12, 40 to 49 is 2, 50 to 59 is 4. c. A histogram has number of hours on the x-axis, and frequency on the y-axis. 0 to 9 is 8, 10 to 19 is 3, 20 to 29 is 10, 30 to 39 is 12, 40 to 49 is 4, 50 to 59 is 1. d. A histogram has frequency on the x-axis, and number of hours on the y-axis. 0 to 9 is 1, 10 to 19 is 6, 20 to 29 is 15, 30 to 39 is 12, 40 to 49 is 2, 50 to 59 is 4.
Please select the best answer from the choices provided
A B C D
Solution
To determine the correct histogram, analyze the frequency table and match the description of the histogram with the given data:
Data Recap:
- 0-9 hours: Frequency = 1
- 10-19 hours: Frequency = 6
- 20-29 hours: Frequency = 15
- 30-39 hours: Frequency = 12
- 40-49 hours: Frequency = 2
- 50-59 hours: Frequency = 4
Analysis:
A histogram represents the frequency of data values for different ranges (bins). Typically, the x-axis represents the bins (number of hours), and the y-axis represents the frequencies. Let's match the choices:
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Option A: The x-axis represents frequency, and the y-axis represents number of hours. This does not match the standard representation, and the values listed do not align with the data.
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Option B: The x-axis represents the number of hours, and the y-axis represents frequency. The frequencies are:
- 0-9 = 1
- 10-19 = 6
- 20-29 = 15
- 30-39 = 12
- 40-49 = 2
- 50-59 = 4
This is an accurate representation.
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Option C: The x-axis represents the number of hours, and the y-axis represents frequency. However, the frequencies listed (e.g., 0-9 = 8, 10-19 = 3) do not match the data.
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Option D: The x-axis represents frequency, and the y-axis represents number of hours. This does not match the standard representation, and the data does not align.
Correct Answer: B
Would you like additional details or visual representation?
5 Related Questions:
- How would the shape of the histogram change if all frequencies doubled?
- Can the mean and median of the data be determined from this histogram?
- How would the histogram change if a bin size of 5 hours was used instead?
- What is the cumulative frequency for hours ≤ 29?
- What is the mode of the data based on this histogram?
Tip: A histogram is useful for visualizing the distribution of data, and the bin sizes significantly influence the histogram's appearance. Always ensure the bins are consistent and non-overlapping.
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Math Problem Analysis
Mathematical Concepts
Data Analysis
Histograms
Frequency Tables
Formulas
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Theorems
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Suitable Grade Level
Grades 6-8